It's hard to say. I have not seen a signed note yet in my research. I have only seen them listed as 18XX. I would guess 1870's -1880's.
I don't think I have to tell you what an awesome note you have! ANY Obsolete from Montana in that condition is nice even if it is a remainder. I have only seen remainders for this note, so if you do find one with a date and signatures please keep us informed.
There's a proof of the front of this note in ABNC's American Paper Money Collection, representing the state of Montana. It was printed circa 1870s, while Montana was still a territory. The vignette is titled "Horse Fair," engraved by James Smillie from a painting by French artist Rosa Bonheur: http://www.metmuseum.org/toah/works-of-art/87.25 It also appears on a $5 obsolete from Bulls Head Bank in New York. Beautiful note, LostDutchman!